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Old March 17th 07, 11:11 PM posted to rec.radio.amateur.antenna
Cecil Moore[_2_] Cecil Moore[_2_] is offline
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First recorded activity by RadioBanter: Mar 2007
Posts: 3,521
Default VSWR doesn't matter?

Owen Duffy wrote:
The magnitude of a reflection (zero or otherwise) is *always* and *only*
related to whether the ratio of V to I for the "thing" (whether it is
another line, a lumped circuit or some combination) attached to the end
of the line is equal to Zo. The magnitude is calculated from V/I (Zl) and
Zo using a well known expression.


I assume you are talking about virtual reflection
coefficients based on virtual V/I impedances, something
that has gotten hams into conceptual trouble for any
number of years. Let's take a look at the S-Parameter
equations.

Port 1 | Port 2
---Z0---+---Z1---
a1-- | --a2
--b1 | b2--

b1 = s11*a1 + s12*a2
b2 = s21*a1 + s22*a2

As you probably know, s11 is a *physical* reflection
coefficient involving unequal impedances.
s11 = (Z1-Z0)/(Z1+Z0)
Z0 and Z1 are physical impedances, not virtual
impedances, i.e. *NOT* merely a V/I ratio.

a1 is the voltage wave incident upon Port 1.
s11*a1 is the reflection from Port 1.

If Z1 Z0, there exists an impedance discontinuity.
s11 0, and s11*a1 0, i.e. there exist reflections.
This is why I say: If there is a physical impedance
discontinuity, then reflections exist.

If reflections are to be canceled, then s12*a2
must be equal in magnitude and 180 degrees out of
phase with reflection s11*a1. Note that for
reflections to be canceled, they must first exist.

s12*a2 is the voltage not reflected from Port 2.

All this is covered in HP Application Note 95-1,
"S-Parameter Techniques" available from:

http://www.sss-mag.com/pdf/an-95-1.pdf
--
73, Cecil http://www.w5dxp.com